Abstract and Applied Analysis

Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative

Ai-Min Yang, Cheng Zhang, Hossein Jafari, Carlo Cattani, and Ying Jiao

Full-text: Open access

Abstract

The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 395710, 5 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425047794

Digital Object Identifier
doi:10.1155/2014/395710

Mathematical Reviews number (MathSciNet)
MR3170404

Zentralblatt MATH identifier
07022305

Citation

Yang, Ai-Min; Zhang, Cheng; Jafari, Hossein; Cattani, Carlo; Jiao, Ying. Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 395710, 5 pages. doi:10.1155/2014/395710. https://projecteuclid.org/euclid.aaa/1425047794


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